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arXiv · 2106.08214

Efficient multi-level hp-finite elements in arbitrary dimensions

Philipp Kopp·Ernst Rank·Victor M. Calo·Stefan Kollmannsberger
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Abstract

We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized implementations. We only operate on the bounding faces of finite elements without considering their lower-dimensional topological features and demonstrate the potential of the presented methods using a newly written open-source library. First, we analyze a Fichera corner and show that the framework does not increase runtime and memory consumption when compared against the classical p-version of the finite element method. Then, we compute a transient example with dynamic refinement and derefinement, where we also obtain the expected convergence rates and excellent performance in computing time and memory usage.

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Philipp Kopp, Ernst Rank, Victor M. Calo, Stefan Kollmannsberger. 2021-06-15. Efficient multi-level hp-finite elements in arbitrary dimensions. https://doi.org/10.1016/j.cma.2022.115575

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